A008706 Coordination sequence for 3.3.3.4.4 planar net.
1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275
Offset: 0
Examples
G.f. = 1 + 5*x + 10*x^2 + 15*x^3 + 20*x^4 + 25*x^5 + 30*x^6 + 35*x^7 + ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers
- Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also arXiv:1803.08530.
- Branko Grünbaum and Geoffrey C. Shephard, Tilings by regular polygons, Mathematics Magazine, 50 (1977), 227-247.
- Tom Karzes, Tiling Coordination Sequences
- Reticular Chemistry Structure Resource, cem
- N. J. A. Sloane, The uniform planar nets and their A-numbers [Annotated scanned figure from Gruenbaum and Shephard (1977)]
- Index entries for linear recurrences with constant coefficients, signature (2,-1).
Crossrefs
Essentially the same as A008587.
List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).
First differences of A005891.
Programs
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Magma
[0^n+5*n: n in [0..50] ]; // Vincenzo Librandi, Aug 21 2011
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Mathematica
Join[{1}, LinearRecurrence[{2, -1}, {5, 10}, 100]] (* Jean-François Alcover, Dec 13 2018 *) -
PARI
a(n)=0^n+5*n \\ Charles R Greathouse IV, Mar 19 2015
Formula
From Paul Barry, Jul 21 2003: (Start)
G.f.: (1 + 3*x + x^2)/(1 - x)^2.
a(n) = 0^n + 5n. (End)
G.f.: A(x) + 1, where A(x) is the g.f. of A008587. - Gennady Eremin, Feb 21 2021
E.g.f.: 1 + 5*x*exp(x). - Stefano Spezia, Jan 05 2023
Comments